The primary aim of this study is to determine whether 4 cycles of Taxol given after 4 cycles of postoperative Adriamycin (A) and cyclophosphamide (C) will more effectively prolong disease-free survival and survival than do 4 cycles of postoperative AC alone in patients with operable breast cancer who have one or more histologically positive axillary lymph nodes. Patients should have no evidence of metastatic disease and should have undergone either lumpectomy plus axillary node dissection or total mastectomy plus axillary node dissection. Following stratification by number of positive axillary nodes, tamoxifen administration, and type of surgery, patients will be randomly assigned to one of two groups. All patients in both groups who undergo lumpectomy will receive postoperative radiotherapy after completion of their assigned chemotherapy and after any toxicity has resolved.